Quantum Mechanics: Superposition of 2 States?

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Discussion Overview

The discussion revolves around the concept of superposition in quantum mechanics, specifically questioning whether superpositions are limited to two states or can include more. Participants explore the implications of probability amplitudes and the Born rule within this context.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that if quantum mechanics is a realistic probability theory, then superpositions may only involve two states at a time, based on the way probability amplitudes combine.
  • Another participant counters that for some quantum systems, superpositions can indeed involve more than two states.
  • A request for clarification is made regarding examples or references that support the claim of superpositions involving more than two states, along with a question about the interpretation of the Born rule.
  • A correction is issued regarding the mathematical representation of probability amplitudes, with a reference to a previous discussion where this claim was addressed.

Areas of Agreement / Disagreement

Participants exhibit disagreement on the nature of superpositions in quantum mechanics, with some asserting that only two states are involved while others argue for the possibility of more than two states. The discussion remains unresolved.

Contextual Notes

There are limitations in the assumptions made about the nature of probability amplitudes and the interpretation of the Born rule, which are not fully explored in the discussion.

kurt101
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Assuming Quantum mechanics is a probability theory that describes something real (which should be our first presumption), is there ever only a superposition of 2 states?

The reason I ask this is because:

For calculating the probability of an outcome you square the sum of the probability amplitudes.

If you have outcomes with probability amplitudes a, b, c; then you would get a probability of aa + ab + ac + bb + ba + bc + cc + ca + cb. You don't ever see a term like abc or aab for example.

So assuming QM is a realistic probability theory, you are multiplying all of the ways A can happen plus all of the ways B can happen plus all of the ways C can happen. Assuming these different terms are treated as actual realistic instance possibilities, doesn't this imply that when considering one instance a superposition of only aa or ab or ac or ba or bb or bc or ca or cb or cc is actually possible? In other words you don't actually see superpositions beyond two states at a time.
 
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kurt101 said:
Assuming Quantum mechanics is a probability theory that describes something real (which should be our first presumption), is there ever only a superposition of 2 states?

The quick answer, for some quantum systems, no -- there can be more than 2 states as part of the superposition.
 
StevieTNZ said:
The quick answer, for some quantum systems, no -- there can be more than 2 states as part of the superposition.
Can you provide a reference, example, or anything that might me be able to understand the longer answer? And are you implying that the Born rule is violated or just my interpretation of it is?
 
kurt101 said:
If you have outcomes with probability amplitudes a, b, c; then you would get a probability of aa + ab + ac + bb + ba + bc + cc + ca + cb.

No, you don't. I've already corrected you on this in the other thread where you made this claim; see here:

https://www.physicsforums.com/threa...y-qm-is-incomplete.956222/page-3#post-6064334

Since your OP is based on a mistaken premise, I am closing this thread.
 

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